Results from Blind Test Series 1, part of the Collaborative Computational Project in Wave Structure Interaction (CCP-WSI), are presented. Participants, with a range of numerical methods, simulate blindly the interaction between a fixed structure and focused waves ranging in steepness and direction. Numerical results are compared against corresponding physical data. The predictive capability of each method is assessed based on pressure and run-up measurements. In general, all methods perform well in the cases considered, however, there is notable variation in the results (even between similar methods). Recommendations are made for appropriate considerations and analysis in future comparative studies.

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Highlights • Two different approaches, 2-D OpenFOAM and Lagrangian wave-current simulations, are used to model focussed wave groups and sheared currents simultaneously in a controlled manner, and produce input conditions for 3-D OpenFOAM models to investigate wavecurrent-structure interactions. • Good agreement between numerical results and experimental data is obtained, indicating that both approaches are capable of replicating experimental wave-current flows, and accurately modelling interactions between surface piercing cylinders and focussing waves on sheared currents. • The performance of both approaches is evaluated in terms of accuracy and computational effort required. • It is found that the method of coupling 3-D CFD and Lagrangian models is computational slightly cheaper and slightly more accurate because of the use of a smaller computationally domain and the iterative wave-current generation in the faster Lagrangian model.

A new description of two-dimensional continuous free-surface flows in Lagrangian coordinates is proposed. It is shown that the position of a fluid particle in such flows can be represented as a fixed point of a transformation in R 2. Components of the transformation function satisfy the linear Euler-type continuity equation and can be expressed via a single function analogous to an Eulerian stream function. Fixedpoint iterations lead to a simple recursive representation of a solution satisfying the Lagrangian continuity equation. Expanding the unknown function in a smallperturbation asymptotic expansion we obtain the complete asymptotic formulation of the problem in a fixed domain of Lagrangian labels. The method is then applied to the classical problem of a regular wave travelling in deep water, and the fifthorder Lagrangian asymptotic solution is constructed, which provides a much better approximation of steep waves than the corresponding Eulerian Stokes expansion. In contrast with early attempts at Lagrangian regular-wave expansions, the asymptotic solution presented is uniformly valid at large times.